Heat engines move heat from a source to a sink. Heat engines can be divided into two fundamental classes distinguished by the direction in which heat moves. Heat spontaneously flows “downhill”, that is, to lower temperatures. As with the flow of water, “downhill” heat flow can be harnessed to produce mechanical work, as illustrated by internal-combustion engines, e.g. Devices that move heat “uphill”, that is, toward higher temperatures, are called heat pumps. Heat pumps necessarily consume power. Refrigerators and air conditioners are examples of heat pumps. Most commonly used heat pumps employ a working fluid (gaseous or liquid) whose temperature is varied over a range that includes the temperatures of both the source and sink between which heat is pumped. This temperature variation is commonly accomplished by compression of the working fluid. Bernoulli heat pumps effect the required temperature variation by exploiting the well-known Bernoulli principle, according to which random molecular motion (temperature and pressure) is converted into directed motion (macroscopic fluid flow) while leaving the total kinetic energy unchanged. Bernoulli conversion occurs most commonly when the cross-sectional area of a fluid flow is reduced, as in a Venturi-shaped duct wherein the cross-sectional area of fluid flow passes through a minimum along the flow path. The fluid may either be a gas or a liquid. Prior examples of such are described by C. H. Barkelew in U.S. Pat. No. 3,049,891, “Cooling by flowing gas at supersonic velocity”, Oct. 21, 1960; and by V. C. Williams in U.S. Pat. No. 3,200,607, “Space Conditioning Apparatus, Nov. 7, 1963.
The directed motion must increase in order to maintain a constant mass flux as the cross-sectional area decreases, as in a garden-hose nozzle. Such conversion occurs spontaneously, that is without additional energy, by the local reduction of the random molecular motion, which is reflected in the temperature and pressure. Whereas compression consumes power, Bernoulli conversion does not. Though Bernoulli conversion itself consumes no power, the fluid nozzling usually implies strong velocity gradients within the heat-sink flow. Velocity gradients imply viscous losses. Thus, a challenge central to the development of Bernoulli heat pumps is the discovery and exploitation of structures and materials that facilitate heat transfer while minimizing viscous losses.
It has been found recently in thermoacoustic applications that mixtures of rare gases possess anomalously small viscosities. Discussion of this development and additional references can be found in M. E. H. Tijani, J. C. H. Zeegers, and A. T. A. M. de Waele, “Prandtl number and thermoacoustic refrigerators”, Journal of the Acoustical Society of America, 112, No. 1, pp. 134-143, (July, 2002).
The conventional efficiency metric for heat pumps is the “coefficient of performance” (CoP) which is the ratio of heat-transfer rate to the power consumed. In a Bernoulli heat pump, the principal source of power consumption is viscous friction within the Venturi neck, where the flow velocity is greatest. Both the temperature difference driving the heat transfer and the viscous dissipation are proportional to the square of the flow velocity. Two properties of the working fluid are critical to the efficiency of a Bernoulli heat pump—its thermal conductivity and its viscosity. A dimensionless property of gases, called the Prandtl number, is fundamentally the ratio of these two properties. The CoP thus benefits directly from the use of materials characterized by small Prandtl numbers. The above-mentioned findings by Tijani et al in the context of thermoacoustic devices that mixtures of rare gases possess unusually small Prandtl numbers has now been applied in accordance the present invention, as a novel application of this finding to the improvement of the operation of Bernoulli heat pumps and methods.